Circular Scale of Time Applied in Classifying the Quantum-Mechanical Energy Terms Entering the Framework of the Schrödinger Perturbation Theory

• 作者: S. Olszewski
• 来源期刊: 量子信息科学期刊(英文)
• 学科: 数学
• 关键词: CIRCULAR SCALE of TIME Quantum-Mechanical Energy TERMS Complementary Relations Schr?dinger’s Perturbation Theory
• 年，卷（期）: 2011,（3）
• 页码范围: 142-148
• 页数: 7页
• 分类号: O1

摘要

The paper applies a one-to-one correspondence which exists between individual Schr?dinger perturbation terms and the diagrams obtained on a circular scale of time to whole sets of the Schr?dinger terms belonging to a definite perturbation order. In effect the diagram properties allowed us to derive the recurrence formulae giving the number of higher perturbative terms from the number of lower order terms. This recurrence formalism is based on a complementary property that any perturbation order N can be composed of two positive integer components Na , Nb combined into N in all possible ways. Another result concerns the degeneracy of the perturbative terms. This degeneracy is shown to be only twofold and the terms having it are easily detectable on the basis of a circular scale. An analysis of this type demonstrates that the degeneracy of the perturbative terms does not exist for very low perturbative orders. But when the perturbative order exceeds five, the number of degenerate terms predominates heavily over that of nondegenerate terms.